578 



A DYNAMICAL THEORY OP THE ELECTROMAGNETIC FIELD. 



(93) If we combine the equations of Magnetic Force (B) with those of 

 Electric Currents (C), and put for brevity 



dF dG dH^j d ^_.. d L, d ^ = . 

 dx dy dz ~ dx* dy* dz* 



(63), 



(64). 



If the medium in the field is a perfect dielectric there is no true conduction, 

 and the currents p, q', r are only variations in the electric displacement, or, 

 by the equations of Total Currents (A), 



, df , dq . dh 



*-% *~% r= Tt < 65 >- 



But these electric displacements are caused by electromotive forces, and by the 

 equations of Electric Elasticity (E), 



P = kf, Q = kg, R = Tch (66). 



These electromotive forces are due to the variations either of the electro- 

 magnetic or the electrostatic functions, as there is no motion of conductors in 

 the field ; so that the equations of electromotive force (D) are 



_ 



'It dx 



dG 

 ~dt 



~dy 



dH 



s 



dt 



1 



dz 



(67). 



(94) Combining these equations, we obtain the following : 



.(68). 



